Pointwise estimates for minimizers of some non-uniformly degenerate functionals (Q913224)

We prove Hölder regularity and the Harnack inequality for non-uniformly degenerate functionals of the type \(F(u,\Omega)=\int_{\Omega}F(x,Du)dx\). We adapt the techniques used by \textit{M. Giaquinta} and \textit{E. Giusti} [Acta Math. 148, 31-46 (1982; Zbl 0494.49031); Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1, 79-107 (1984; Zbl 0541.49008)], \textit{E. DiBenedetto} and \textit{N. S. Trudinger} [ibid., 295-308 (1984; Zbl 0565.35012)], and \textit{G. Modica} [Ann. Mat. Pura Appl., IV. Sér. 142, 121-143 (1985; Zbl 0596.49008)], by equipping \(R^ n\) with a metric constructed in order to take into account the special non-uniformly degeneration of F.